Disturbance-Free-Payload is a novel spacecraft architecture proposed to achieve perfect vibration isolation performance of space applications. In this paper, the object under study is a DFP system in which a flexible umbilical connection between the support module (SM) and the payload module (PM) is introduced for data, power and fluid transfer. Bead model accounting for properties of mass and flexibility, is utilized to model the flexible umbilical. With incorporation of bead model, six degree-of-freedom multibody rigid-flexible dynamics for the DFP system is established via Newtonian mechanics. Along with rotational coupling between solar panels and SM, translational coupling, in particular, is taken into consideration since there is a stringent requirement on relative position between PM and SM. Based on the accurate motion equations of the DFP system, simulation studies are conducted to gain insight of the impact of umbilical connection and translational coupling on pointing performance of the DFP system. Simulation results validate effectiveness of DFP configuration in isolating vibrations transmitted from SM to PM. Besides, umbilical connection plays an important part in degrading pointing performance of PM whereas it exerts little impact on SM. Moreover, translational coupling leads to significant pointing performance degradation for both PM and SM.